Two semi-infinite bodies in contact with each other

2 Two semi-infinite bodies in contact with each other 

We will consider the two semi-infinite bodies shown in Fig. 2.24, which have different, but constant, initial temperatures d01 and d02- Their material properties Ax, a1 and A2, a2 are also different. At time t = 0 both bodies are brought into (thermal) contact with each other along the plane indicated by x = 0. After a very short period of time an average temperature is reached along the plane. Heat flows from body 1 with the higher initial temperature to body 2 which has a lower temperature. The transient conduction process described here serves as a model for the description of short-time contact between two (finite) bodies at different temperatures. Examples of this include the touching of different objects with a hand or foot and the short-time interaction of a heated metal body with a cooled object in reforming processes. 

The heat conduction equation holds for both bodies and is 

For the solution, we assume the contact temperature m at x = 0 to be independent of t. As will be shown this assumption is valid and enables a simple solution to the problem to be found. The problem is split into two parts whose solutions have already been discussed in section 2.3.3.1 A temperature distribution appears in each body, which develops beginning with the constant initial temperatures 0i and 02, respectively, when the surface temperature jumps to the constant value m. 

The assumption of a time independent contact temperature m was therefore appropriate. Its position depends on the thermal penetration coefficients 

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